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# Electrostatics

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1. Electrostatics Static electricity is the buildup and eventual release of charge in an object due to the movement of electrons. It is different from current electricity which is the constant flow of electrons through a material.

2. Electrons can move from one atom to another and from one material to another because they are located in electron clouds around the nucleus. Protons CANNOT move from one material to another because the protons are tightly held in the nucleus. • Objects can obtain one of two types of charge: • A positively-charged object develops if an object loses electrons • A negatively-charged object develops if an object gains electrons

3. Fundamental Rule for Electrostatic Charge • Opposite charges attract • Like charges repel • This is true for large-scale objects and for atomic particles (protons, electrons, ions) • Electric charge is measured in coulombs (C) • A proton has a charge of +1.60 x 10-19 C (+e) • An electron has a charge of -1.60 x 10-19 C (-e)

4. Coulomb’s Law determines the amount of attraction or repulsion there is. Fc = kq1q2/r2 Fc = electric force (N) q1 = charge of one particle (C) q2 = charge of second particle (C) k = proportionality constant (8.99 x 109 Nm2/C2) r = distance between charges (m) Coulomb’s Law is also expressed this way. Fc = (1/4πε0)q1q2/r2 ε0 = permittivity constant (8.85 x 10-12 C2/Nm2)

5. Referrring to the diagram to the left, what is the net force acting on Q3 by Q1 and Q2?

6. Electric Fields Many forces can move things without any type of contact. Gravity moves objects without any contact as long as the object is in the Earth’s gravitational field. Gravity is a “force field” Force field – a region in space in which an object can be placed and forces will be exerted on the object without contact Electrical charges can move other electrical charges without making contact; therefore, they have electric fields. Electric fields are represented with lines that extend out from the center; the closer the lines, the stronger the field.

7. Field lines are directional, depending on the sign of the charge (Q). To determine the direction of the field, imagine the existence of a positive test charge (P) close to the charge in question (Q). If Q is positive, P will be repelled. The field lines move outward. If Q is negative, P will be attracted. The field lines move inward.

8. Rules for Field Lines • Pattern indicates the direction of the field in a given region (tangent to point on line) • Concentration of lines indicates the strength of the field • Arrow indicates the direction of the field (positive to negative) Figure (a) represents an electricdipole – two equal charges of opposite sign.

9. Test Charge (q) Point Charge (Q) Electric Field Exerted on a Charge The electric field exerted on a test charge is calculated as the force per unit of charge. It is analogous to acceleration… a = F/m a = acceleration (m/s2) F = gravitational force (N) m = mass (kg) E = F/q E = electric field (N/C) F = electric force (N) q = electric charge (C) The larger the mass, the larger the force exerted by gravity The larger the test charge, the larger the force exerted by point charge

10. What is the electric field strength at a point in space where a proton experiences an acceleration of 1 million “g’s”? (mass of proton = 1.67 x 10-27 kg; charge of proton = 1.60 x 10-19 C)

11. Reminder: Electric field lines always go from positive to negative regardless of the force on the charge. If the test charge in the field is positive, the field is in the same direction as the force (Figure “b”) If the test charge in the field is negative, the force is is in the opposite direction (Figure “c”)

12. Electric Field Around a Charge Think about your experience with gravity…the strength of the gravitational field decreases as you move away from the Earth. The strength of the electric field around a point charge decreases as you move away from the charge Test Charge (q) We know that… E = F/q If F = kqQ/r2 Then E = (kqQ/r2)/q E = kQ/r2 k = proportionality constant Q = magnitude of point charge r = distance to point charge Point Charge (Q) Therefore, the electric field at a given distance r can be measured independent of the magnitude of q

13. Two point charges are separated by a distance of 10.0 cm. One has a charge of -25 μC and the other +50 μC. Determine the magnitude and direction of the electric field at a point P between the two charges that is 2.0 cm from the negative charge.

14. Conductors and Insulators Conductors – a material in which electrons move freely from one atom to another and throughout the material as a whole Insulators –a material in which electrons are relatively stationary and do NOT freely move throughout the material

15. How Objects Obtain Charge • Charging by Friction (balloon on head) Triboelectric Series Occurs when there is friction between two different objects. They can be conductors or insulators. Electrons move to the material that “wants” the electrons more.

16. How Objects Obtain Charge 2. Charging by Polarization (balloon with paper) Occurs when a charged object is brought close to an insulator. Since electrons cannot move freely, atoms will turn themselves so that their similar side will be turned away from the object Since the near side is oppositely charged, the object as a whole attracts.

17. How Objects Obtain Charge 3. Charging by Conduction (electroscope, electrophorus) When a charged object makes contactwith a neutral conductor, electrons will move accordingly until the charge is equally distributed. Insulators can also be charged by contact, but since electrons do not move freely, the charge remains localized.

18. How Objects Obtain Charge 4. Charging by Induction (electroscope, electrophorus) When a charged object is brought close to a neutral conductor, electrons in the conductor will group up on one side of the neutral object “inducing” a charge. If the conductor is touched when a charge is induced, electrons will move to neutralize the induced charge. This electron movement actual gives the object a real charge.

19. Electric Potential The comparison continues…. In figure “a”, the rock has potential energy. In figure “b”, assume that the test charges Q and 2Q are positive. Why would they have potential energy? The positive charges “want” to move off of the plate on the left and move to the plate on the right.

20. With the charge… PE pos = KE neg ∆KE = -∆PE With the rock… PEtop = KE bot ∆KE = -∆PE In the same way that the larger rock has more potential energy, the larger charge also has more potential energy.

21. Electric Potential – the electric potential energy per unit charge V = PE/q V = Electric Potential (Volts or J/C) PE = Potential Energy (J) q = charge (C) Potential Difference – the difference in electric potentials between two locations. Also known as the voltage Vba = Vb - Va = PEb / q - PEa / q

22. We know that Vba = (PEb - PEa) / q and W = ∆KE = -∆PE So, Vba = -Wba / q We also know that W = Fd and E = F / q So, W = qEd Therefore, Vba = -(qEd) / q Vba = -Ed

23. E = - V / d E = Electric Field (N/C or V/m) V = Potential Difference (V) d = distance (m) The electric field increases as the voltage across the plates increase, but it decreases as the distance between the plates decreases.

24. When an electron in a television tube is accelerated from rest through a potential difference of 5000 V… • What is the change in potential energy of the electron? • What is the speed of the electron at the other end of the tube? • What is the electric field across the tube if the distance across the tube is 50 cm?

25. Equipotential Lines What do the lines on this map represent? Lines of equal elevation. No work needed to walk along line. Close lines mean the elevation changes dramatically.

26. Equipotential lines show were the electric potential around charged objects is equal. They are always perpendicular to electric field lines. No work needed to move charge along equipotential line. Lines that are close together that potential difference is great in short distance.

27. Electric Potential around Point Charges The electric field around a point charge is: E = kQ/r2 The electric field is determined by the strength of the charge but also the distance away from it. The electric potential around a point charge is: V = kQ/r If you double the distance from the point charge, The electric potential is ½ the original amount, but the electric field is ¼ the original amount.

28. Because electric potential is a scalar (like energy), direction does not matter. However, positive charges have positive potentials and negative charges have negative potentials (like energy). The total electric potential is the sum of all of the potentials. V = Σ kQ / r

29. What is the electric potential at point A and the electric potential at point B due to charges Q1 and Q2?

30. Capacitance Capacitors are devices that can store electric charge and then release it in a short burst of charge. They consist of two conductive materials that are placed near each other but not touching. Figure (a) shows a capacitor made up of parallel plates that are separated by a layer of air. Figure (b) shows two conductive layers separated by an insulating material

31. A capacitor loads up with a potential difference (voltage) when opposite charges get established on the different plates. Since the plates are separate but not touching, there is no way initially for the charge to move from one plate to the other. The voltage will eventually become large enough to overcome the gap between the plates resulting in a sudden movement of charge (discharge).

32. C = Q / V Q = charge (C) C = capacitance (farad) V = voltage (V) Capacitance – the ability of an object to store electrical charge. Measures the amount of charge that can be held for a given voltage Capacitance is determined by the gap between the plates and the area of the plates. Some capacitors have dielectric materials which are inserted in the air gap to improve the insulating property between the plates C = Kε0A / d C = capacitance (F) K = dielectric constant ε0 = permittivity constant (8.85 x 10-12 C2/Nm2) A = area of one plate (m2) d = distance between plates (m)

33. A capacitor has plates that are 20 cm x 3.0 cm and are separated by a gap of 1.0 mm of air. • What is the capacitance? • What will be the charge on the plates if a 12-V battery is connected across the plates? • What is the magnitude of the electric field between the plates? • How big would the plates have to be to get a capacitance of 1.0 F?

34. Energy Storage in Capacitors The potential energy stored in a capacitor is equal to the work that is done to move charge to the plates of the capacitor. PE = W = VQ As more charge gets built up on the capacitor, more work is needed to move charge onto the plates. The total work needed to move all of the charge is equal to the average voltage across the capacitor during the process Average V = (Vf + 0) / 2 = ½Vf PE = ½VfQ Q = CV PE = ½CV2 PE = Energy (J) C = Capacitance (F) V = Voltage (V)

35. A camera flash unit stores energy in a 150-μF capacitor at 200 V. How much electric energy can be stored?

36. Charge in Batteries Batteries consist of two different types of metals and a medium that allows electrons to move. Oxidation occurs at the carbon electrode when it to lose electrons making it positive. Reduction occurs at the zinc electrode when it gains electrons becoming negative. Voltage is created between terminals based on the amount of charge on each of the terminals. What makes batteries have different voltages? When is a battery dead?

37. Since the electrons have the potential to move, all they need is a path to return. Circuit – a complete path from one battery terminal to another through a conductive material The flow of electrons can be used to make electrical devices function provided they become part of the circuit.

38. Which of the following would cause the bulb to light up? Light bulbs are designed to allow the flow electrons in one way, passing through the filament, and out a different way.

39. Circuits are represented by schematic designs. The actual flow of electrons is from the negative terminal to the positive terminal. The historical convention for current flow is as positive charge flowing from the positive terminal to negative terminal. Current – the amount of charge that passes a given point in a conductor I = Q / ∆T I = Current (Amperes) ∆Q = change in charge (C) ∆T = elapsed time (s)

40. Current, Voltage, and Resistance If voltage is analogous to a change in elevation, current is analogous to a flowing river. As elevation increases, the flow of water increases. As voltage increases, the flow of charge (current) increases. Therefore, current is directly proportional to voltage.

41. Resistance impedes flow. Obstacles in a river slow down the flow of water Conductors can have electrical resistance that slows down the flow of charge. As resistance increases, current decreases. Therefore, current is inversely proportional to resistance.

42. Ohm’s Law I = V / R Or V = IR V = voltage (V) I = current (A) R = resistance (Ohms)

43. Clarifications about Voltage, Current and Resistance • Batteries are sources of constant voltage, not constant current. The current out of a batteries changes depending on the resistance of the circuit. • Resistance is a property of a device or conducting material. Voltage, however, is applied “across” a device. Current is a “response” to the voltage across a device depending on the resistance. • Current is directional, but it is not a vector, It always moves parallel to a wire. • Current and charge does not get used up by a device in a circuit. The charge that leaves one terminal of a battery travels through the entire circuit and returns to the other terminal. • Electric potential energy gets used up by a specific device. Resistances have voltage “drops” where electric potential energy is converted to other forms of energy (light, heat, etc.)

44. Electric Power Devices in a circuit that are “voltage drops“ convert the potential energy in the charge to other types of energy. Motors convert electric energy to mechanical energy (movement) Light bulbs convert electrical energy to radiant energy (light) Heaters convert electrical energy to thermal energy (heat) All of these devices use current at different rates which is their power We know power is amount of work done per unit of time P = W / t In an electrical device, work comes from the potential energy in the charge, so P = PE / t

45. Recall the relationship between potential energy, charge, and voltage V = PE / Q PE = QV So, P = QV / t Since Q / t = I P = IV P = power (Watts) I = current (A) V = voltage (V) Since V = IR P = I(IR) P = I2R And since I = V/R P = (V/R)V P = V2/R

46. Since resistance is a property of a conducting material, it is determined by physical characteristics of the material. R = ρL / A R = resistance (Ω) ρ = resistivity coefficient (Ωm) L = length of wire (m) A = cross-sectional area (m)

47. A hair dryer draws 7.5 A when plugged into a 120-V line. • What is its resistance? • How much charge passes through it in 15 minutes? • What is the length of copper wire running through the hair dryer assuming it is 14-gauge wire with a diameter of 1.6 mm?

48. Batteries and other devices provide electromotive force (emf) to circuits. Electromotive force (E) – the process of transforming chemical energy to electrical energy. Think of it as the peak voltage of a battery (measured in volts) Batteries also have internal resistance (r) that develops when current is drawn from the battery. This results in a slighty lower voltage provided by the battery. Terminal voltage – the actual voltage provided by a battery when in a circuit V = E - Ir

49. Series Circuit A series circuit is one that has only one path through which current can travel Current flows equally through all three resistors even though they are not necessarily the same. There is no buildup of electrons at higher resistors. I = constant Since charge loses its all of its energy by the time it gets back to the battery, the voltage drops across all three resistors is equal to the voltage gain in the battery. V = V1 + V2 + V3

50. Equivalent resistance – the sum of the individual resistances in the circuit V = V1 + V2 + V3 IR = IR1 + IR2 + IR3 IR = I (R1 + R2 + R3) Req = R1 + R2 + R3 In a series circuit: Current constant Voltages add Resistances add